In Cuba there are banknotes with values of 3, 10 and 20 pesos. Using only these banknotes, what is the largest amount that can not be formed?

1 Answer
Apr 4, 2017

17

Explanation:

What an intriguing question!

Note that the first 10 multiples of 3 end on every possible digit from 0 to 9.

3," "6," "9," "12," "15," "18," "21," "24," "27," "30

Arranged so the units are in order from 0 to 9:

30," "21," "12," "3," "24," "15," "6," "27," "18," "9

Every number from 20 upwards can be written either as a multiple of 3 or 10, or as the sum of a multiple of 10 and a multiple of3.

20 = 10+10
21 = 7 xx3
22 = 10+12 = 10 +4 xx3
23 = 10+3
25 = 10+15 = 10+5xx3
26 = 20+2xx3
28 = 10 +18 = 10 +6xx3
29 = 10+3xx3
31 = 10 +21 = 10 +7xx3
32 = 20+12 = 20+4xx3 etc.....

What about the numbers less than 20 that cannot be formed with 3 and 10?

19 = 10+9 = 10+3xx3
18 = 6xx3
17 = ???????????????